Other voices have also entered the fray. The Federal-Postal Coalition, made up of 21 union and employee and manager associations, wrote this week to the deficit committee's co-chairs, Sen. Patty Murray (D-Wash.) and Rep. Jeb Hensarling (R-Texas), warning against deeper cuts to federal employees' pay and benefits.

Coming after federal workers have already had their pay frozen, the White House deficit reduction proposal is "simply unfair and unacceptable" NTEU President Colleen Kelly said.

But other proposals would call for even deeper cuts.

Sen. Ron Johnson (R-Wisc.) announced his supercommittee recommendations — amounting to $1.4 trillion in cuts over 10 years— earlier this month. Johnson, who serves as the ranking Republican on the Homeland Security and Governmental Affairs subcommittee tasked with overseeing government management, said many of his proposals amount to "common sense."